1. Field of the Invention
The invention relates generally to the field of marine seismic surveying. More specifically, the invention relates to methods for processing signals acquired using streamers having both pressure responsive sensors and motion responsive sensors.
2. Background Art
In seismic exploration, geophysical data are obtained by applying acoustic energy to the earth from an acoustic source and detecting seismic energy reflected from interfaces between different layers in subsurface formations. The seismic wavefield is reflected when there is a difference in acoustic impedance between the layer above the interface and the layer below the interface. When using towed streamers in marine seismic exploration, one or more seismic streamers is towed behind an exploration vessel at a water depth typically between about six to about nine meters, but can be towed shallower or deeper. Hydrophones are included in the streamer cable for detecting seismic signals. A hydrophone is a submersible pressure gradient sensor that converts pressure waves into electrical or optical signals that are typically recorded for signal processing, and evaluated to estimate characteristics of the subsurface of the earth.
In a typical geophysical exploration configuration, a plurality of streamer cables are towed behind a vessel. One or more seismic sources are also normally towed behind the vessel. The seismic source, which typically is an airgun array, but may also be a water gun array or other type of source known to those of ordinary skill in the art, transmits seismic energy or waves into the earth and the waves are reflected back by reflectors in the earth and recorded by sensors in the streamers. Paravanes are typically employed to maintain the cables in the desired lateral position while being towed. Alternatively, the seismic cables are maintained at a substantially stationary position in a body of water, either floating at a selected depth or lying on the bottom of the body of water, in which case the source may be towed behind a vessel to generate acoustic energy at varying locations, or the source may also be maintained in a stationary position.
After the reflected wave reaches the streamer cable, the wave continues to propagate to the water/air interface at the water surface, from which the wave is reflected downwardly, and is again detected by the hydrophones in the streamer cable. The water surface is a good reflector and the reflection coefficient at the water surface is nearly unity in magnitude and is negative in sign for pressure signals. The waves reflected at the surface will thus be phase-shifted 180 degrees relative to the upwardly propagating waves. The downwardly propagating wave recorded by the receivers is commonly referred to as the surface reflection or the “ghost” signal. Because of the surface reflection, the water surface acts like a filter, which creates spectral notches in the recorded signal, making it difficult to record data outside a selected bandwidth. Because of the influence of the surface reflection, some frequencies in the recorded signal are amplified and some frequencies are attenuated.
For pressure recording of vertically propagating waves, maximum attenuation will occur at frequencies for which the propagation distance between the detecting hydrophone and the water surface is equal to one-half wavelength and an integer multiple thereof. Maximum amplification will occur at frequencies for which the propagation distance between the detecting hydrophone and the water surface is one-quarter wavelength and odd integer multiples thereof. The wavelength of the acoustic wave is equal to the velocity divided by the frequency, and the velocity of an acoustic wave in water is about 1500 meters/second. Accordingly, the location in the frequency spectrum of the resulting spectral notch is readily determinable. For example, for a seismic streamer at a depth of 7 meters, and waves with vertical incidence, maximum attenuation will occur at a frequency of about 107 Hz and maximum amplification will occur at a frequency of about 54 Hz.
U.S. Pat. No. 7,359,283 issued to Vaage et al. and assigned to an affiliate of the assignee of the present invention describes methods for using streamers having both pressure responsive sensors and motion responsive sensors. By having both types of sensors it is possible to reduce the effects of the ghost on the detected seismic signals. Performing the method described in the Vaage et al. '283 patent in particular requires that signals generated by the motion responsive sensors have their amplitudes adjusted for the angle of incidence of the seismic signals at the time of detection by the motion responsive sensors. Such angle of incidence will depend on, among other factors, the seismic velocities of the various formations below the water bottom and the location of the seismic sensors with respect to the seismic energy source. The method of the Vaage et al. '283 patent may be performed in two dimensions, that is, in a direction along one or more individual streamers, or in three dimensions, that is, for surveys conducted using a plurality of laterally spaced apart streamers towed by a seismic vessel such that angle of incidence is calculated in both the longitudinal (along the streamer) direction and transverse (cross-line) to the streamer direction. In three dimensions, the seismic signals have an angle of incidence at each of the motion responsive sensors on each streamer that depends on the distance of each sensor from the source in both the longitudinal and transverse (cross-line) directions.
The application of the method of the Vaage et al. '283 patent in three dimensions requires sufficiently dense spatial sampling of the seismic signals in both the longitudinal and cross-line directions to avoid spatial aliasing. Spatial aliasing may result in inaccurate estimates of the incidence angle, and thus inaccurate scaling of the motion responsive signals. Incorrect scaling may lead to inaccurate separation of the seismic signals into upgoing and downgoing components. In practice, for marine streamer surveys the spatial sampling interval in the longitudinal direction (along the streamer) is typically 12.5 meters, which is sufficient to limit spatial aliasing effects within the seismic frequency range. However, the spatial sampling (distance between streamers) in the cross-line direction is rarely less than 50 meters and is more often 100 meters. For a 50 meter sampling interval, spatial aliasing is encountered for frequencies above 15 Hz, which is well within the seismic frequency range. Therefore, in order to use the method of the '283 patent in three dimensions extensive interpolation is required in the cross-line direction. Such interpolation can be computationally expensive. However, if the angle of incidence in the cross-line direction is close to vertical, it is possible to use the two dimensional implementation of the method in the '283 patent for the signals from each individual streamer without materially degrading the result. A similar consideration applies to the procedure in the '283 patent for simulating the low frequency part of the motion responsive sensor signal.
Incidence angles of the seismic signals at the receivers will generally decrease with respect to reflected seismic energy travel time because the energy travel path is relatively longer in the vertical direction as contrasted with the distance between the source and each seismic receiver. Furthermore, for typical marine seismic acquisition geometries for which the maximum cross-line offset is of the order of 500 meters or less, incidence angles in the cross-line direction are likely to be very small for deep (long travel time) seismic reflectors. For such seismic reflectors the two dimensional approximation can be used. However, this approximation may not be useful for shallower (smaller seismic travel time) targets.